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arXiv:2007.16065 · New Journal of Physics

Dynamical structure factors of a two-dimensional Fermi superfluid within random phase approximation

Huaisong Zhao, Xiaoxu Gao, Wen Liang, Peng Zou, Feng Yuan

Published Jul 31, 2020• 19 citations
arXivHTMLPDF

Abstract

Abstract Based on random phase approximation, we numerically calculate dynamical structure factors of a balanced two-dimensional (2D) Fermi superfluid, and discuss their energy, momentum and interaction strength dependence in the 2D BEC–BCS crossover. At a small transferred momentum, a stable Higgs mode is observed in the unitary 2D Fermi superfluid gas where the particle–hole symmetry is not satisfied. Stronger interaction strength will make the visibility of the dispersion of Higgs mode harder to be observed. We also discuss the dimension effect and find that the signal of the Higgs mode in two dimension is more obvious than that in 3D case. At a large transferred momentum regime, stronger interaction strength will induce the weight of the molecules excitation increasing, while in verse the atomic one decreasing, which shows the pairing information of Fermi superfluid. The theoretical results qualitatively agree with the corresponding quantum Monte Carlo data.

DOI
10.1088/1367-2630/abab3d

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Abstract Based on random phase approximation, we numerically calculate dynamical structure factors of a balanced two-dimensional (2D) Fermi superfluid, and discuss their energy, momentum and interaction strength dependence in the 2D BEC–BCS crossover. At a small transferred momentum, a stable Higgs mode is observed in the unitary 2D Fermi superfluid gas where the particle–hole symmetry is not satisfied. Stronger interaction strength will make the visibility of the dispersion of Higgs mode harder to be observed. We also discuss the dimension effect and find that the signal of the Higgs mode in two dimension is more obvious than that in 3D case. At a large transferred momentum regime, stronger interaction strength will induce the weight of the molecules excitation increasing, while in verse the atomic one decreasing, which shows the pairing information of Fermi superfluid. The theoretical results qualitatively agree with the corresponding quantum Monte Carlo data.
We leverage random phase approximation and unbiased auxiliary-field quantum Monte Carlo methods to compute dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the collective excitations of the system to generate robust benchmark results and to shed light into fermionic superfluidity in the strongly correlated regime. In particular we are motivated by a recent paper suggesting that the Higgs mode can be detected in the spectrum of spin fluctuations. Despite the fact that we are somewhat limited by finite-size effects, our study indeed pinpoints a clear peak in the spin channel at low momentum, but a detailed analysis suggests that such a peak, though certainly interesting, does not correspond to the Higgs mode. We propose a different explanation for the shape of the spin structure factor. However, our results clearly show that the Higgs mode can be detected in the density channel at very small wave vectors, although very good resolution is necessary.
We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6 Li or 40 K atoms using Bragg spectroscopy.
We use mean-field theory to investigate the dynamics of superfluid fermions. This thesis includes our two works. The first one is to study Josephson oscillations and self-trapping of superfluid fermions in a double-well potential with time-dependent Bogoliubov-de Gennes equations. We investigate the behaviour of a two-component Fermi superfluid. We numerically solve the time-dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for different potential barriers and initial conditions. In the weak link limit the results agree with a two-mode model where the relative population and the phase difference between the two wells obey coupled nonlinear Josephson equations. A more complex dynamics is predicted for large amplitude oscillations and large tunneling. The second one is to calculate the dynamic structure factor of unitary fermions. We have studied the dynamic structure factor of unitary fermions both at zero and finite temperature using the Bogoliubov-de Gennes theory and also Superfluid Local Density Approximation. We have derived the expression of the linear response function and the dynamic structure factor in the random phase approximation. At zero temperature, the SLDA+RPA formalism indeed provides a better accuracy at low momentum transfer and also its static structure factor is closer to quantum Monte Carlo value than that in BdG+RPA; however SLDA seems to give worse results for the molecular excitations at large momentum transfer. We have discussed the role of temperature and the comparison between SLDA and BdG, as well as with experimental data. The analysis is still at a preliminary level, but it suggests that mean-field theories can indeed be used to extract quantitative information about the order parameter and the excitations of the system by two-photon Bragg scattering experiments.
We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation approach at zero temperature, and find their dynamical characters across the phase transition from a balanced conventional Bardeen-Cooper-Schrieffer (BCS) superfluid to a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a Bose-Einstein-condensate-like regime of the Fermi superfluid, dynamic structure factors can help distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition from BCS to Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum where the collective phonon excitation acquires a finite width, and also a relatively strong atomic excitation at a large transferred momentum, because of the existence of unpaired Fermi atoms. Our results can be used to differentiate Sarma superfluid from BCS superfluid.
The static and dynamic structure factors of an interacting Fermi gas along the BCS-BEC crossover are calculated at momentum transfer ℏ k higher than the Fermi momentum. The spin structure factor is found to be very sensitive to the correlations associated with the formation of molecules. On the BEC side of the crossover, even close to unitarity, clear evidence is found for a molecular excitation at ℏ 2 k 2 /4 m , where m is the atomic mass. Both quantum Monte Carlo and dynamic mean-field results are presented.
Interfacing unbiased quantum Monte Carlo simulations with state-of-the-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of U(1)\text{U}(1)U(1) broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art generalized random phase approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for generalized random phase approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight into the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.